Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems
Abstract
We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon.
Keywords
Cite
@article{arxiv.nlin/0104044,
title = {Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems},
author = {Raul Toral and Claudio R. Mirasso and Emilio Hernandez-Garcia and Oreste Piro},
journal= {arXiv preprint arXiv:nlin/0104044},
year = {2009}
}
Comments
10 pages including 12 postscript figures, revtex. Additional work in http://www.imedea.uib.es/Nonlinear . The paper with higher-resolution figures can be obtained from http://www.imedea.uib.es/PhysDept/publicationsDB/date.html